Results 11 to 20 of about 230,228 (280)
Rigidity and gluing for Morse and Novikov complexes [PDF]
, 2003 We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function.
Cornea, Octav, Ranicki, Andrew
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Fractal and Fractional, 2023 This work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furthermore,
Yujie Tang +4 more
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Lagrangian submanifolds and Lefschetz pencils [PDF]
, 2004 Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold.
Auroux, Denis +2 more
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Homotopy properties of smooth functions on the Möbius band
Pracì Mìžnarodnogo Geometričnogo Centru, 2019 Let $B$ be a M\"obius band and $f:B \to \mathbb{R}$ be a Morse map taking a constant value on $\partial B$, and $\mathcal{S}(f,\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\partial B$ and preserving $f$ in the sense that $f\circ h ...
Iryna Kuznietsova, Sergiy Maksymenko
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The nudged elastic band method for effective natural image patches analysis
AIP Advances, 2020 We used sampled data from a well-established database of natural images to construct a density estimator, which is designed to act as a Morse function.
Kewen Cha, Shuang Wang, Shengxiang Xia
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Umbilical Submanifolds and Morse Functions [PDF]
Nagoya Mathematical Journal, 1972 Let Mn be a differentiable manifold (of class C∞). By a Morse function on Mn we mean a differentiable function whose critical points are all non-degenerate. If f is an immersion of Mn into a Euclidean space Rm, we may obtain Morse functions on Mn in the following way.
Nomizu, Katsumi, Rodríguez, Lucio
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Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics [PDF]
, 2019 We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their ...
Krajňák, Vladimír, Wiggins, Stephen
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The computation of the index of a Morse function at a critical point
International Journal of Mathematics and Mathematical Sciences, 1988 A theoretical approach in computing the index of a Morse function at a critical point on a real non-singular hypersurface V is given. As a consequence the Euler characteristic of V is computed. In the case where the hypersurface is polynomial and compact,
Takis Sakkalis
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The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology [PDF]
, 2016 The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions.
Rot, Thomas O.
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Computing Persistent Homology by Spanning Trees and Critical Simplices
Research, 2023 Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the dataset, that is,
Dinghua Shi +3 more
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